A mathematical model for population distribution III: An analytical approach to pray-predator systems

The present paper is a continuation of the work described in Elias (2023) and Elias (2024) which attempt to develop a deterministic simulation for phenomena occurring in Regional Science, incorporating demographic, economic, geographical etc. variables to a mathematically simulated deterministic system. Herein, such systems are approximated by a generalization of the Helmholtz wave equation, providing the possibility to better understand the dynamic influence of the environment and of the interaction between the variables within the system, thus making possible the discrimination between inertial, isolated (closed) and (open-general) dynamic cases. A simulation concerning population systems is presented, applied on prey – predator systems, without utilizing the Lotka – Volterra equations. For these systems the analytically derived expressions for the equations of motion (temporal) and distribution (spatiotemporal) are produced.